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EXAMPLE 1

Can the triangles be proven congruent with the information given in the diagram? If so, state the postulate or theorem you would use.

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EXAMPLE 1

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  1. Can the triangles be proven congruent with the information given in the diagram? If so, state the postulate or theorem you would use. The vertical angles are congruent, so two pairs of angles and a pair of non-included sides are congruent. The triangles are congruent by the AAS Congruence Theorem. EXAMPLE 1 Identify congruent triangles SOLUTION

  2. There is not enough information to prove the triangles are congruent, because no sides are known to be congruent. Two pairs of angles and their included sides are congruent. The triangles are congruent by the ASA Congruence Postulate. EXAMPLE 1 Identify congruent triangles

  3. C F, BC EF A D, GIVEN ABCDEF PROVE EXAMPLE 2 Prove the AAS Congruence Theorem Prove the Angle-Angle-Side Congruence Theorem. Write a proof.

  4. In the diagram at the right, what postulate or theorem can you use to prove that ? Explain. RSTVUT STATEMENTS REASONS Given S U Given RS UV The vertical angles are congruent RTSUTV for Examples 1 and 2 GUIDED PRACTICE SOLUTION

  5. RTSUTV for Examples 1 and 2 GUIDED PRACTICE ANSWER Therefore are congruent because vertical angles are congruent so two pairs of angles and a pair of non included side are congruent. The triangle are congruent by AAS Congruence Theorem.

  6. ABC GIVEN m 1 + m 2 + m 3 = 180° PROVE STATEMENTS REASONS Rewrite the proof of the Triangle Sum Theorem on page219as a flow proof. 1. Parallel Postulate 1. Draw BDparallel to AC. 2. m 4 + m 2 + m 5 2. = 180° Angle Addition Postulate and definition of straight angle , 4 3. 1 5 3. 3 Alternate Interior Angles Theorem m 4 m 5 4. m 1 = , m 3 = 4. Definition of congruent angles 5. m 1 + m 2 + m 3 5. Substitution Property of Equality = 180° for Examples 1 and 2 GUIDED PRACTICE

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